Pork butt, despite its colorful name, does not come from anywhere near the butt (or behind) of the pig. In fact, quite the opposite. Pork butt is a cut of meat from the shoulder of the pig. Seriously.
Pork Butt Versus Pork Shoulder
So where does the cut of pork called pork shoulder come from? Also the shoulder.
Technically "pork butt" (as well as Boston butt, a different name for more or less the same cut), comes from the thicker section of the shoulder where there is more intense marbling (that means fat running through the meat).
Cuts labeled "shoulder" (including a "picnic shoulder") are from the thinner, triangle-shaped end of the shoulder (it would be attached to the butt if they weren't commonly separated into smaller cuts).
How to Cook Pork Butt
Both pork butt and pork shoulder cuts need long, slow cooking and are great barbecued, braised, or used as stew meat. This is because they are from a hard-working section of the body, carrying around all that hog weight and developing great flavor—this is notably true of pastured pork from pigs raised in environments where they can walk freely.
In short, you can, if necessary, use them interchangeably in most recipes. Pork shoulder is a bit better if the final plan is to slice or chop the meat and have it hold its shape, while pork butt has more intense marbling and thus is particularly well suited for barbecue, specifically making pulled pork or other recipes where you want the final dish to fall apart more or less.
Pork butt is delicious in spicy stews such as New Mexican Carne Adovada, this Green Chili, or a classic Posole since the fat in it helps really spread that chile flavor around, and the chunks of meat will tend to get even more tender than pork shoulder does. Again, it's all about the marbling.
Wait, But What About the Actual Butt?
That area of the pig we might think of the actual butt?
The behind? The bottom? That's where the ham—cooked fresh or cured or smoked—is from. Ham is the thigh and most of the gluteus maximus (that's why it's so meaty).
Note: Many styles and regional variations exist in butchery, so when in doubt, ask your butcher for specifics.